101)

If 3x - 2y + 3 = 0, then what will be the value of 27x³ + 54xy + 30 - 8y³ ?

SSC CHSL 2021

A)

3

B)

57

C)

-27

D)

-57

102)

The value of a³ + b³ + c³ - 3abc, when a = 125, b = 127 and c = 129, is:

SSC CHSL 2021

A)

3752

B)

4572

C)

4752

D)

4725

103)

If \(a = \frac{\sqrt{5}+2}{\sqrt{5}-2}\) and \(b ={\sqrt5-2\over\sqrt5+2}\), then the value of 2a² + 2b² - 5ab is equal to:

SSC CHSL 2021

A)

693

B)

649

C)

635

D)

639

104)

If (7x - 10y) = 8 and xy = 5, then what is the value of 49x² + 100y²?

SSC CHSL 2021

A)

623

B)

764

C)

632

D)

746

105)

If \(x^2+{1\over x^2}=83\), x > 0, then the value of \(x^3-\frac{1}{x^3}\) is:

SSC CHSL 2021

A)

675

B)

576

C)

756

D)

746

106)

A,B, C and D are four positive numbers such that A is \(\frac{3}{4}\) times of B, B is \(\frac{4}{5}\) times of C, and C is \(\frac{3}{8}\) times of D. If the average of 4 times of A and 7 times of D is 316, then the average of all the four numbers A, B, C and D is:

SSC CHSL 2021

A)

36

B)

38

C)

28

D)

34

107)

If x² + (4 - √3)x - 1 = 0, then what is the value of \(x^2+\frac{1}{x^2} \)?

SSC CHSL 2021

A)

21 - 8√3

B)

17 - 8√3

C)

9 - 8√3

D)

21 - 12√3

108)

If \(x+{1\over x}=\sqrt{13}\), then one of the values of \(x^3-\frac{1}{x^3}\) is:

SSC CHSL 2021

A)

36

B)

32

C)

4√13

D)

4√11